Answer:
It will take 6.68 years to reach the $10,000 goal.
Explanation:
As the deposit of $1,000 per year is a form of the annuity payment.
We will use the following formula in order to calculate the numbers of year required to reach the goal
Future value of Annuity = Annuity payment x ( ( ( 1 + interest rate )^numbers of years ) - 1 ) / Interest rate
Where
Future value of Annuity = Target amount = $10,000
Annuity payment = Yearly deposti = $1,000
Interest rate = 14%
Numbers of years = n = ?
Placing values in the formula
Future value of Annuity = Annuity payment x ( ( ( 1 + interest rate )^numbers of years ) - 1 ) / Interest rate
$10,000 = $1,000 x ( ( ( 1 + 14% )^n ) - 1 ) /14%
$10,000 x 14% = $1,000 x ( ( ( 1.14 )^n ) - 1)
$1,400 = $1,000 x ( ( ( 1.14 )^n ) - 1)
$1,400 / $1,000 = ( ( 1.14 )^n ) - 1
1.4 = ( ( 1.14 )^n ) - 1
1.4 + 1 = 1.14^n
2.4 = 1.14^n
Log 2.4 = n x Log 1.14
n = Log 2.4 / Log 1.14
n = 6.681525965
n = 6.68 years
It will take 6.68 years to reach the $10,000 goal.
